See image — Isomerism and Stereochemistry Chemistry Question

💡 Solution & Explanation

Concept: In butatriene (H2C=C=C=CH2), the molecule is a cumulene with an even number of cumulated double bonds (3 double bonds, 4 carbons). For cumulenes with an even number of double bonds, the two terminal CH2 groups lie in the SAME plane (unlike allene where they are perpendicular). The geometry is planar overall. However, looking at the structural drawing carefully: the left CH2 group has one H drawn going upper-left (with an arrow indicating l1 measurement) and one H drawn going lower-left. The right CH2 group has one H upper-right and one H lower-right. The molecule is drawn in a V or X shape at the left carbon, suggesting a 3D perspective where the two H atoms on the left carbon are spread out (one going up-left and one going down-left in a wedge/dash arrangement). Key geometric point: l1 is drawn as the distance from the upper-left H to the upper-right H, spanning the full length of the molecule horizontally (the arrow for l1 goes all the way across the top). l2 is drawn from the lower-left H to the lower-right H, but the lower-left H is positioned closer to the center of the molecule (it comes off the left carbon at a downward angle toward the right), so l2 measures a shorter horizontal projection. More precisely: The left CH2 is drawn with one H going far upper-left and one H going lower but not as far left. The arrow for l1 spans the full width (H upper-left to H upper-right), while l2 spans a shorter diagonal (lower-left H to lower-right H). Since the lower H atoms are angled inward (closer to the carbon chain), the H...H distance l2 is measured along a path that is more angled/diagonal and shorter in horizontal extent than l1. Alternatively interpreting the diagram: l1 is the distance between the two H atoms that are farther apart (both pointing outward away from the molecular axis), and l2 is the distance between H atoms that are closer (pointing more inward or at a smaller spread angle). The arrows in the image show l1 as a longer span and l2 as a shorter span based on the angles of the C-H bonds drawn. Since the upper H atoms on both ends are directed more outward (larger angle from the molecular axis as drawn), l1 > the span of l2. Wait - but the answer is C (l1 < l2). Re-examining: l1 goes from H (upper-left) to H (upper-right) - this is drawn as a straight horizontal arrow across the TOP. l2 goes from H (lower-left) to H (lower-right) - drawn across the bottom. The lower-left H is drawn pointing downward-left from the left carbon, and the lower-right H is pointing downward-right from the right carbon. In the perspective drawing, the lower H atoms are in the plane of the page and spread wider, while the upper H atoms are drawn with a perspective that makes them appear closer together at the top. The 3D arrangement of butatriene (planar, with both CH2 in the same plane) means the H-H distances depend on the exact geometry. Given the drawing, l2 (bottom H to bottom H) spans a wider distance because those H atoms are drawn further apart (the bottom arrow is longer in the diagram), making l1 < l2. Why other options fail: (a) l1 = l2 would require both pairs of H atoms to be equidistant, which is not the case given the asymmetric perspective drawing. (b) l1 > l2 would mean the top H atoms are farther apart, contradicting the diagram. (d) l2 = 2l1 is a specific numerical ratio not supported by geometry. Therefore, the correct answer is C.